Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

<image>

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
from sys import stdin, stdout

arr = ["row", "col"]

def solve(g, n, m, flag):
    newG = []
    ans = []
    for i in range(n):
        newG.append([0] * m)
    
    for i in range(n):
        k = min(g[i])
        newG[i] = [k] * m
        ans.extend([arr[flag] + " {}".format(i + 1)] * k)
    
    for i in range(m):
        k = 0
        while min([newG[u][i] for u in range(n)]) < min([g[u][i] for u in range(n)]):
            for u in range(n):
                newG[u][i] += 1
            k += 1
        if [newG[u][i] for u in range(n)] != [g[u][i] for u in range(n)]:
            return -1, []
        else:
            ans.extend([arr[1 - flag] + " {}".format(i + 1)] * k)
    
    else:
        return len(ans), ans


n, m = [int(item) for item in stdin.readline().strip().split()]

g = []

for i in range(n):
    g.append([int(item) for item in stdin.readline().strip().split()])

g2 = []

for i in range(m):
    g2.append([g[k][i] for k in range(n)])
    
a, ans1 = solve(g, n, m, 0)
b, ans2 = solve(g2, m, n, 1)

if a == -1 or b == -1:
    print(-1)
else:
    if a <= b:
        print(a)
        for item in ans1:stdout.write(str(item) + "\n")
    else:
        print(b)
        for item in ans2:stdout.write(str(item) + "\n")